It's all very hand wavy and no one has implemented unilateral exits in prod afaict. 

And, if they are reusing addresses and moving your balance/state forward with you offline, unilateral exit relies on them not doing that when they decide to rug/shotgun kyc.

You mean if you use a static deposit address instead of being online and creating a new address + presigned unilateral exit transaction for every deposit?

I guess in that case you need to trust that you will be able to claim your deposit.

I also don't know how unilateral exit works for lightning deposits.

How do you get the presigned unilateral exit transactions when you're offline and the federation receives on your behalf?